Statistical properties of flexible polymers with controlled molecular weights (length of arms) and branching patterns (topology) has been attracting strong interest. Basically, the lattice enrichment algorithms are suitable for simulating this kind of subject because they allow direct estimation of the total configuration number. However, it is difficult to apply this kind of algorithm for polymers with highly complicated structures, namely the comb-polymers. One of the difficulties is that the efficiency of simulation is severely limited. In this paper, a previously reported improvement technique is revisited, enhanced, and combined with several new ideas for developing a modified algorithm, which can solve such a situation. The validation and performance evaluation of the modified algorithm is presented. The algorithm is then applied to small scale polymer combs. In particular, the value of the critical exponent related to the configuration number is estimated on these combs. The result obtained for an H-shaped polymer is in accordance with previous simulations and a theoretical prediction formula already proposed. Possibilities for the future extension of the algorithm are briefly discussed.